A manufacturer wishes to make tee-shirts for the band Dixie Chicks. They sell for $15 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money M she will receive for the shirts in terms of the number n of machines she decides to set up (assuming she sells all the shirts she makes)

Question

Mathematics

Romeo

11 November, 12:27

A manufacturer wishes to make tee-shirts for the band Dixie Chicks. They sell for $15 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money M she will receive for the shirts in terms of the number n of machines she decides to set up (assuming she sells all the shirts she makes)

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Marisa Liu · Answer 1

M = 3000n (20 - n) dollars.

Step-by-step explanation:

Given that, each machine sets up in one day.

Therefore, n number of machines will take n days to set up.

Now, there are 20 days' time to deliver all the t-shirts.

And the machines are turned on after all the n machines are set up.

So, all the n machines will work for (20 - n) days and producing each machine 200 shirts in one day, then one machine will produce 200 (20 - n) number of t-shirts and n machines will produce 200n (20 - n) number of t-shirts in the remaining (20 - n) days.

Now, the selling price for each t-shirt is $15.

Therefore, the total amount of money M she will receive will be, M = 15 * 200n (20 - n) = 3000n (20 - n) dollars. (Answer)